Question

Select all radical expressions that are equivalent to 5 2/3 ( its an improper fraction)

√15

(3√5)^2

3√5^2

3√10

Answer 1

In order to select all radical expressions that are equivalent to
`5^{(2)/(3)},` you have to represent all given expressions as powers.

Option A.

`√(15)=15^{(1)/(2)}.`

Option B.

`(\sqrt[3]{5})^2=(5^{(1)/(3)})^2=5^{(2)/(3)}.`

Option C.

`\sqrt[3]{5^2}=(5^2)^{(1)/(3)}=5^{(2)/(3)}.`

Option D.

`\sqrt[3]{10}=10^{(1)/(3)}.`

Answer: correct choices B and C